Asynchronous Gathering of Robots with Finite Memory on a Circle under Limited Visibility

TL;DR

This paper studies the problem of robots gathering on a circle with limited visibility and finite memory, extending previous work to asynchronous settings and analyzing the impact of these constraints.

Contribution

It extends prior gathering algorithms to asynchronous models with finite memory and limited visibility, addressing an open problem in distributed robot coordination.

Findings

Proposes a new gathering algorithm under asynchronous scheduler.

Analyzes the limitations imposed by finite memory and limited visibility.

Provides conditions for successful gathering in the specified model.

Abstract

Consider a set of $n$ mobile entities, called robots, located and operating on a continuous circle, i.e., all robots are initially in distinct locations on a circle. The \textit{gathering} problem asks to design a distributed algorithm that allows the robots to assemble at a point on the circle. Robots are anonymous, identical, and homogeneous. Robots operate in a deterministic Look-Compute-Move cycle within the circular path. Robots agree on the clockwise direction. The robot's movement is rigid and they have limited visibility $\pi$, i.e., each robot can only see the points of the circle which is at an angular distance strictly less than $\pi$ from the robot. Di Luna \textit{et al}. [DISC'2020] provided a deterministic gathering algorithm of oblivious and silent robots on a circle in semi-synchronous (\textsc{SSync}) scheduler. Buchin \textit{et al}. [IPDPS(W)'2021] showed that, under full visibility, $\mathcal{OBLOT}$ robot model with \textsc{SSync} scheduler is incomparable to $\mathcal{FSTA}$ robot (robots are silent but have finite persistent memory) model with asynchronous (\textsc{ASync}) scheduler. Under limited visibility, this comparison is still unanswered. So, this work extends the work of Di Luna \textit{et al}. [DISC'2020] under \textsc{ASync} scheduler for $\mathcal{FSTA}$ robot model.